Generation of a Gaussian a random process with Matlab

[confused_engineer]

TL;DR Summary

I am working unsing the software Matlab trying to construct realizations of gaussian stochastic processes. However, the results I obtain don't look gaussian.

Hello everyone.

I am currently working with Matlab. I have a 2D gaussian kernel constructed using the muKL technique (first attached figure). I want to use it to generate realizations of a gaussian random process using the KL theorem. For that, I obtain then all eigenvectors and eigenvalues of said kernel and multiply the square root of each eigenvalue by the corresponding eigenvector and a number extracted from a N(0,1) and add all of them together to obtain the realization. I do this a number of times and obtain what can be seen in the second attached figure. However, if I plot the first and second half of each realization differently over a 2D surface, I obtain what can be seen in the third attached figure, which doesn't look gaussian at all. Can someone please tell me what am I doing wrong?

I will too attach a sample code with a smaller covariance matriz so that if anyone is interested, can take a look (since the kernel is too big to upload)

Best regards.
Confused_engineer.

 

[mmwave]

Hello Confused_engineer,

Thank you for sharing your work and asking for feedback. It seems like you are on the right track with using the KL theorem to generate realizations of a Gaussian random process. However, there are a few things that could potentially be causing the issue you are seeing in the third attached figure.

First, it is important to make sure that your kernel is properly constructed and that the eigenvectors and eigenvalues are calculated correctly. If there are any errors in these steps, it could lead to incorrect realizations.

Second, it is possible that the number of realizations you are generating is not enough to accurately represent the Gaussian process. The KL theorem states that the number of realizations should be equal to the number of eigenvalues, so make sure you are generating enough realizations for your specific case.

Lastly, it is possible that there is an issue with how you are plotting the data in the third figure. It is important to make sure that the data is being plotted correctly and that any scaling or transformations are applied consistently across all realizations.

I would recommend double-checking your code and calculations, and also trying to generate more realizations to see if that improves the results. If you are still having trouble, it might be helpful to reach out to a colleague or mentor for further assistance.

Best of luck with your work!